Minimal Unavoidable Set with 49 permutations

Everything about Sudoku that doesn't fit in one of the other sections

Re: Minimal Unavoidable Set with 13 permutations

Postby coloin » Fri May 06, 2011 12:05 am

Interesting indeed.

Code: Select all
+---+---+---+
|..3|...|..2|
|.8.|9..|.7.|
|5..|...|1..|
+---+---+---+
|.6.|4.9|...|
|...|..8|...|
|...|67.|.4.|
+---+---+---+
|..1|...|3..|
|.7.|..4|.8.|
|2..|...|..5|
+---+---+---+   2 isomorphic grid solutions, UA 60.


This pseudopuzzle with a UA 60 posted after Oceans - and also found by you has an interesting property.

Its not that the the 2 sol. are isomorphic.

Its because almost all of the resultant {+1} puzzles are hard ++

I found large unavoidables in Easter Monster when it came out.

I have often wondered if this was coincidental - or do all the n-1 subpuzzles in hard ++ puzzles tend to have

either
large UA in the solution grid of the hard puzzle
or
high valancy

Despite one of the clues in all of the resulting puzzlesfrom the above pseudopuzzle having valancy 2........ i have a hunch that many or all of the subpuzzles from our hardest puzzles have high valancy and largeish unavoidables.

Perhaps have a look at
Code: Select all
........6..5..18...9...8.7....8.2.....3.1.2..4..5.3....6.....9...83..1..7.......4 # tarx0075


C
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Posts: 1629
Joined: 05 May 2005

Re: Minimal Unavoidable Set with 13 permutations

Postby dobrichev » Fri May 06, 2011 10:27 am

coloin wrote:Despite one of the clues in all of the resulting puzzlesfrom the above pseudopuzzle having valancy 2........ i have a hunch that many or all of the subpuzzles from our hardest puzzles have high valancy and largeish unavoidables.

Perhaps have a look at
Code: Select all
........6..5..18...9...8.7....8.2.....3.1.2..4..5.3....6.....9...83..1..7.......4 # tarx0075



Below are the multivalent UA hit by a single clue. Wide screen.
Hidden Text: Show
Code: Select all
#tarx0075
........6..5..18...9...8.7....8.2.....3.1.2..4..5.3....6.....9...83..1..7.......4       22
        1       8       91      53      #Clue,pos,numUA,maxUAsize
                3       .8....9....5..18...9.6.8.7..1.8.2...8.3.1.26.4295637...6.1.7.9.9.83.6127731...6.4       #nPerm,UA
                3       .8....9....5..18...9.6.8.7..1.8.2...8.341.26.4295637...6.1...9.9.83.6127731...6.4       #nPerm,UA
                3       ...........5..18...9.6.8.7....8.2.....3.1.2.54..5.37...6.....9...83..1.773...56.4       #nPerm,UA

        2       11      114     49      #Clue,pos,numUA,maxUAsize

        3       14      157     50      #Clue,pos,numUA,maxUAsize
                3       ..7.3.9.6..57..8...9...8.7..1.872....73.1.2..4..5.3.1..64....9.95834.1..7.19....4       #nPerm,UA

        4       15      311     52      #Clue,pos,numUA,maxUAsize
                3       ..7.3.9.66.5791...39.6.8.71..68.2..9873.1.2.54295.3.18.6.18..9.9.83..1..731.....4       #nPerm,UA
                3       1.7.....66.57.1....9.6.8.715168.2...87341.2..4295.3.18.6.18..9.9.83..1..7.1....84       #nPerm,UA
                3       ....3.9.6..5.91...39...8.71...8.2..9..3.1.2.5429563718.6.18..9.9.83.61..731.....4       #nPerm,UA
                3       ..7.3...6.45..1...39...8.71...8.2.....3.192..4..56371..64187.9.9.83..1.7731.....4       #nPerm,UA
                3       ..7.34..6..57.1....9..58.71..68.2.....3.192..4295.3.18.6..8..9.9.83..1..7.......4       #nPerm,UA
                3       1..2..9.6..5..1....9...8.71.1.8.23....3.1.2..42.5.3.18.6.18..9.9.83..1..7.1.2...4       #nPerm,UA

        5       19      130     54      #Clue,pos,numUA,maxUAsize

        6       23      8       53      #Clue,pos,numUA,maxUAsize
                3       ........66.5..18...9.6..47...68.2.....3.1.2.542.5.3....6.1...9...83..1..7.......4       #nPerm,UA

        7       25      126     49      #Clue,pos,numUA,maxUAsize

        8       30      58      49      #Clue,pos,numUA,maxUAsize
                3       1872....66.57.18...9.6.8.71.16.72....73.1.2..4295.3.1..6.....9.9.83..1..7......84       #nPerm,UA
                3       .8..3...6..5..18...9..5847..1...2.....3.192..4295.37...6.....9.9.83.61.773...5684       #nPerm,UA
                3       ..72....66.57.18...9.6.8.71..6..2.....3.1.2..4295.3.18.6.....9.9.83..1..7......84       #nPerm,UA

        9       32      109     52      #Clue,pos,numUA,maxUAsize
                3       ..72....66457.18...92..8.7..1687......3.192..4.95.3....641...9.95834.1..7.19....4       #nPerm,UA
                3       ..72....66457.18...9...8.7...68.......3.192..4295.3....641...9.95834.1..7..9....4       #nPerm,UA
                3       .87.3...66.57.18...9...8.7..1.87....8.3.192..4..5.3....6.....9...83..1..7.......4       #nPerm,UA

        10      38      428     51      #Clue,pos,numUA,maxUAsize

        11      40      4       41      #Clue,pos,numUA,maxUAsize

        12      42      319     52      #Clue,pos,numUA,maxUAsize
                3       ........66.5..183..926.847.5168.2.4...3.1....42.563....6...759...83..1.77.......4       #nPerm,UA
                3       ........66.5..183..926.847.51.8.2.4...3.1....42.5.37...6...759...83..1.77.......4       #nPerm,UA
                3       ...2....66.5..18...926.847..168.2.....3.1....42.563....6....59...83..1.77.......4       #nPerm,UA

        13      45      132     53      #Clue,pos,numUA,maxUAsize
                3       1872....6..57.18...9...8.71...8.2...8.3.1.2...2.5.3.18.6.18..9...83..1..7...25.84       #nPerm,UA
                3       ........6..5..18...9..5847.51.8.2.....3.192.5...563....641...9.9583..1..7.19....4       #nPerm,UA
                3       187.....6..57.18...9...8.71...8.2...8.3.192...2.5.3.18.6.18..9...83..1..7......84       #nPerm,UA
                3       187.....6..57.18...9...8.71...872...873.192.5.2.5.3....6.1...9...83..1..7.......4       #nPerm,UA
                4       .87.3...6..57.18...9...8.7....872...873.192.5.2.5.3....6.1...9...83..1..7.......4       #nPerm,UA
                3       .87.34..6..57.18...9..5847..1.872...8.3.192.....5.3....6.....9...83..1..7.......4       #nPerm,UA

        14      48      17      46      #Clue,pos,numUA,maxUAsize

        15      50      24      44      #Clue,pos,numUA,maxUAsize

        16      55      167     48      #Clue,pos,numUA,maxUAsize

        17      61      41      48      #Clue,pos,numUA,maxUAsize

        18      65      92      49      #Clue,pos,numUA,maxUAsize
                3       1.....9.66.5..18...9.6.8.71516872..9..341.2..42.5.3.18.6.18..9....3..1..7.1....84       #nPerm,UA

        19      66      173     53      #Clue,pos,numUA,maxUAsize
                3       ..7.....66.57.18...9.658.71..68.2.....341.2654..563.18.6..8..93..8..61..7....5684       #nPerm,UA
                3       ........66.5..183..9...8.71..6872.4...341.2..42.5.3.18.6.18..9...8...1..7...25.84       #nPerm,UA
                3       ........6..5..183..9..5847...6872.4...341.2..42.5.3....6.1...9...8...12.7....5..4       #nPerm,UA
                3       ........66.5..183..9...8.7.516872.4...3.1.2..42.5.3...26.....9...8...1..7.......4       #nPerm,UA
                3       ........6.45..18...9...8.7....8.2.....3.1.2.542.563...2641...9...8...1..7.......4       #nPerm,UA

        20      69      225     52      #Clue,pos,numUA,maxUAsize
                3       ........66.57.18...9.6.847..16872.4...341926.42.563....6.1...9...83.....7.......4       #nPerm,UA
                3       ....3...6.45..18...9...8.7....8.2.....3.192.542.563...2641.7.9...83.....73......4       #nPerm,UA

        21      72      125     49      #Clue,pos,numUA,maxUAsize

        22      80      150     52      #Clue,pos,numUA,maxUAsize
                        4       34      3001    54      #maxPerm,numSpecialUA,numUA,maxUAsize

[edit 2: added the values of maxUAsize in the clue header and in the puzzle footer.]

There are 3001 UA, 33 of them have valency (valancy?) of 3, and one have 4.
With some arithmetics the 3001 UA not hit by 21 clues could be compared to average 34000 UA not hit by 16 clues in the 17s list.

Below is the distribution of UA by size. Although the source is the same puzzle with single clue removed, all solutions are compared to each other (instead to original puzzle solution only), and UA completions are counted (instead of complementary fixed clue combinations representing the generating pseudo-puzzle).
Column 1 is the UA size, column 2 is the number of UA, column 3 is the number of distinct (non-isomorphic) UA sets.
Hidden Text: Show
Code: Select all
 4  41152   1
 6  18176   4
 8  10198   11
 9  1880    4
 10 8712    61
 11 3318    65
 12 8300    433
 13 4480    692
 14 8272    2023
 15 6502    2607
 16 9598    4426
 17 8830    4827
 18 11154   6646
 19 12308   8101
 20 14688   10111
 21 16526   11988
 22 19142   14435
 23 22394   17487
 24 26445   21218
 25 31091   25682
 26 36702   30786
 27 43625   37621
 28 51574   45557
 29 60361   54146
 30 71300   64894
 31 80696   74978
 32 92407   86544
 33 103594  97941
 34 116477  110989
 35 126091  121451
 36 137288  133094
 37 143693  139965
 38 146582  143463
 39 148378  145934
 40 143969  142106
 41 135912  134344
 42 123457  122314
 43 109381  108509
 44 90552   89991
 45 72871   72588
 46 56550   56387
 47 38952   38899
 48 25623   25566
 49 14941   14938
 50 8389    8380
 51 3831    3826
 52 1598    1597
 53 521     521
 54 133     133
 55 31      31
 56 4       4

[edit: added column 2 with the number of UA regardless of isomorphism]

Cheers,
MD
Last edited by dobrichev on Sun May 08, 2011 4:19 pm, edited 1 time in total.
dobrichev
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Re: Minimal Unavoidable Set with 13 permutations

Postby coloin » Sun May 08, 2011 9:12 am

Thanks indeed for that. Disappointing in that neither large sets or valency predominated.

I liked to think of it as a very balanced [minimal] puzzle.

Being a diamond puzzle- there are no eliminations for the pms - apart from the simple box/line ones.

Looking at all the n-1 subpuzzles from tarx0075 i found that there was only one clue [actual] insertion that could be performed - although it was not one which a human solver could "see".

8@r3c6 removed = 28 grid solutions - and all these solutions have a 2 @ r6c2 .

Its not clear from your data if all of the clues all have a big unavoidable ??????????

So a repeat analysis of an easy puzzle would probably show one or more clues which didnt have a big unavoidable.

C
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Re: Minimal Unavoidable Set with 13 permutations

Postby dobrichev » Sun May 08, 2011 4:15 pm

coloin wrote:Looking at all the n-1 subpuzzles from tarx0075 i found that there was only one clue [actual] insertion that could be performed - although it was not one which a human solver could "see".

8@r3c6 removed = 28 grid solutions - and all these solutions have a 2 @ r6c2 .

I have code which for a given puzzle creates a table which clue combinations which pencilmarks eliminated.
Number of rows is 2^nClues. For 17-given puzzle processing takes minutes.
Later I lost myself what to do with the data :?

coloin wrote:Its not clear from your data if all of the clues all have a big unavoidable ??????????

I will edit my post and add the maximum UA size in the clue headers also in the puzzle footer.
The maximal sizes per clue are {53,49,50,52,54,53,49,49,52,51,41,52,53,46,44,48,48,49,53,52,49,52}.
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14 permutations

Postby dobrichev » Mon May 09, 2011 12:32 pm

This is the pseudo-puzzle with 14 solutions. Any additional clue from the 58 listed in the second row solves the puzzle uniquely.
Code: Select all
........1......23...4..5.......67..8..1.5..7..2.4..5...5.7..4..3....2.9.8...1...6
56382974.798641..521.37.8694351..92.98.2.36.46.7.98.131.9.36.82.4658.1.7.729.435.


Below are the details for unhit UA in all solutions.
Hidden Text: Show
Code: Select all
#pattern,nClues,nSolutions
........1......23...4..5.......67..8..1.5..7..2.4..5...5.7..4..3....2.9.8...1...6       23      14

#solution,sNumber,nUnavoidables
#UA,uaSize,unique
563829741798641235214375869435167928981253674627498513159736482346582197872914356       1       1
56382974.798641..521.37.8694351..92.98.2.36.46.7.98.131.9.36.82.4658.1.7.729.435.       58      y

672384951185976234934125687593267148461859372728431569256798413317642895849513726       2       4
6.2...................................................2.6........................       4       n
6.....9...........9.....6........................................................       4       n
.7..8.....8..7...................................................................       4       n
.........1..9.....9..1...........................................................       4       n

672384951985176234134925687593267148461859372728431569256798413317642895849513726       3       3
6.2...................................................2.6........................       4       n
.7..8.....8..7...................................................................       4       n
.........9..1.....1..9...........................................................       4       n

682374951175986234934125687593267148461859372728431569256798413317642895849513726       4       5
6.2...................................................2.6........................       4       n
6.....9...........9.....6........................................................       4       n
.8..7.....7..8...................................................................       4       n
.........1..9.....9..1...........................................................       4       n
............98.........................8.9................98.....................       6       n

682374951975186234134925687593267148461859372728431569256798413317642895849513726       5       3
6.2...................................................2.6........................       4       n
.8..7.....7..8...................................................................       4       n
.........9..1.....1..9...........................................................       4       n

972384651185976234634125987593267148461859372728431569256798413317642895849513726       6       2
9.....6...........6.....9........................................................       4       n
.7..8.....8..7...................................................................       4       n

982374651175986234634125987593267148461859372728431569256798413317642895849513726       7       3
9.....6...........6.....9........................................................       4       n
.8..7.....7..8...................................................................       4       n
............98.........................8.9................98.....................       6       n

276384951185976234934125687593267148461859372728431569652798413317642895849513726       8       3
2.6...................................................6.2........................       4       n
.7..8.....8..7...................................................................       4       n
.........1..9.....9..1...........................................................       4       n

276384951985176234134925687593267148461859372728431569652798413317642895849513726       9       3
2.6...................................................6.2........................       4       n
.7..8.....8..7...................................................................       4       n
.........9..1.....1..9...........................................................       4       n

286374951175986234934125687593267148461859372728431569652798413317642895849513726       10      4
2.6...................................................6.2........................       4       n
.8..7.....7..8...................................................................       4       n
.........1..9.....9..1...........................................................       4       n
............98.........................8.9................98.....................       6       n

286374951975186234134925687593267148461859372728431569652798413317642895849513726       11      3
2.6...................................................6.2........................       4       n
.8..7.....7..8...................................................................       4       n
.........9..1.....1..9...........................................................       4       n

682374951175896234934125687593267148461958372728431569256789413317642895849513726       12      3
6.2...................................................2.6........................       4       n
6.....9...........9.....6........................................................       4       n
............89.........................9.8................89.....................       6       n

982374651175896234634125987593267148461958372728431569256789413317642895849513726       13      2
9.....6...........6.....9........................................................       4       n
............89.........................9.8................89.....................       6       n

286374951175896234934125687593267148461958372728431569652789413317642895849513726       14      2
2.6...................................................6.2........................       4       n
............89.........................9.8................89.....................       6       n

Cheers,
MD
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16, 17...

Postby dobrichev » Mon May 09, 2011 9:31 pm

Here is one with 16 permutations, decomposed to UA4s.
Code: Select all
...........1..2.34.3..5.67.....6.1.....4.......2..5.8....3....9.6..1.7..7....8.2. #pseudo-puzzle
58674329197.68.5..2.49.1..83578.9.42198.2736564.13.9.7425.7681.8.92.4.53.1359.4.6 #completion


And here is one with 17 permutations, decomposed to UA4s, UA8, UA11, and UA12.
Code: Select all
........1....23...245........31....6.7.....8.9.....4....6..5..3.8.2...7.1...4.9.. #pseudo-puzzle
39856724.7614..598...81936785..9472.6.43521.9.12786.3542.97.81.5.9.316.4.376.8.52 #completion
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Re: Minimal Unavoidable Set with 13 permutations

Postby Serg » Tue May 10, 2011 7:12 pm

Hi, dobrichev!
I've verified all 3 your last UA sets (one UA58 and two UA59, having valency of 14, 16, 17). They all are weakly minimal UA sets. Fantastic! You are very close to beat both records at once - finding minimal UA sets with maximal valency and finding minimal UA set of maximal size!

So, new maximal valency record for minimal multivalent UA sets is 17 (UA59).

Good luck for new finding!

Serg
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Re: Minimal Unavoidable Set with 13 permutations

Postby coloin » Tue May 10, 2011 9:14 pm

Indeed well found.

Of course you have shown that the exceptionally hard puzzle [tarx0075#SE 11.8] has got large unavoidable sets associated with every clue.

An easy puzzle just doesnt

Code: Select all
+---+---+---+
|...|...|..2|
|..7|..8|4..|
|.4.|..1|.3.|
+---+---+---+
|...|1.2|...|
|..6|.3.|7..|
|7..|4.5|...|
+---+---+---+
|.1.|...|.2.|
|..3|6..|8..|
|2..|...|..5|
+---+---+---+ SE 1.5


not sure what the max unavoidable size with each clue is but....
looking at just 1 in the above puzzle - with the 3@ r8c3 removed - it solves partially to leave 25 cells so certainly less than that.

the implications of this are possibly it shows the mechanism as to how how all the clues combine to define the puzzle.
It is considerably easier to visualise this in an easy puzzle.

C
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Re: Minimal Unavoidable Set with 13 permutations

Postby RW » Wed May 11, 2011 7:06 am

I agree with everyone else, very nice work finding these high valency sets!

coloin wrote:looking at just 1 in the above puzzle - with the 3@ r8c3 removed - it solves partially to leave 25 cells so certainly less than that.


In an easy puzzle such as the one above, removing an arbitrary clue will probably give you a result like that. The puzzle starts with a lot of singles and if you remove a clue unrelated to these, then you can solve a lot even with the clue removed. The puzzle above has 5 hidden singles, one naked single and a couple of locked candidates available in the opening grid. All these moves rely on given clue 2 in r4c6. Remove this clue and none of these singles and locked candidates are available anymore. Now the puzzle has 1242 solutions and not a single cell can be solved.

RW
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puzzle difficulty & largest UA hit by a single clue

Postby dobrichev » Wed May 11, 2011 9:05 am

RW wrote:... All these moves rely on given clue 2 in r4c6. Remove this clue and none of these singles and locked candidates are available anymore. Now the puzzle has 1242 solutions and not a single cell can be solved.


The 1242 solutions came from 191 unhit UA, one of which is UA51- the largest UA hit by a single clue.

Below are the details for the single clue removed, see clue #9.
Hidden Text: Show
Code: Select all
........2..7..84...4...1.3....1.2.....6.3.7..7..4.5....1.....2...36..8..2.......5       22
        1       8       8       33      #Clue,pos,numUA,maxUAsize

        2       11      12      31      #Clue,pos,numUA,maxUAsize

        3       14      24      35      #Clue,pos,numUA,maxUAsize

        4       15      5       24      #Clue,pos,numUA,maxUAsize

        5       19      1       14      #Clue,pos,numUA,maxUAsize

        6       23      52      43      #Clue,pos,numUA,maxUAsize

        7       25      8       32      #Clue,pos,numUA,maxUAsize

        8       30      6       28      #Clue,pos,numUA,maxUAsize

        9       32      191     51      #Clue,pos,numUA,maxUAsize

        10      38      36      45      #Clue,pos,numUA,maxUAsize

        11      40      4       32      #Clue,pos,numUA,maxUAsize

        12      42      75      42      #Clue,pos,numUA,maxUAsize

        13      45      6       23      #Clue,pos,numUA,maxUAsize

        14      48      2       20      #Clue,pos,numUA,maxUAsize

        15      50      26      40      #Clue,pos,numUA,maxUAsize

        16      55      45      30      #Clue,pos,numUA,maxUAsize

        17      61      6       30      #Clue,pos,numUA,maxUAsize

        18      65      2       4       #Clue,pos,numUA,maxUAsize

        19      66      89      45      #Clue,pos,numUA,maxUAsize
                3       ....4...2..7..84...42..1.3....172.6..268397..7.14652.391458..2...3..48.92.8....45       #nPerm,UA
                3       ....4...2..7..84...42..1.3..8.172.6..268397..7.14652..91458..2...3..48.92.8....45       #nPerm,UA

        20      69      18      35      #Clue,pos,numUA,maxUAsize

        21      72      28      43      #Clue,pos,numUA,maxUAsize

        22      80      3       13      #Clue,pos,numUA,maxUAsize
                        3       2       647     51      #maxPerm,numSpecialUA,numUA,maxUAsize
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Re: Minimal Unavoidable Set with 13 permutations

Postby dobrichev » Wed May 11, 2011 9:24 am

Serg wrote:I've verified all 3 your last UA sets (one UA58 and two UA59, having valency of 14, 16, 17). They all are weakly minimal UA sets.


Thank you.

For completeness, below is one with valency of 15.
Code: Select all
...........1..2..3..4.5..6......32.....7....4.1..8..5...3..4..9..5.6..8.2..1..7.. #15 solutions
57943612886.97.54.32.8.19.795864..71632.1589.4.72.93.678.52.61.19.3.74.2.46.98.35 #the UA


4 UA with valency of 17 are found in a pool of ~400K large UA.
~20K completions (generating puzzles) for UA of size 60 are found so far. This means ~40K distinct UA60.
0 UA61.
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19

Postby dobrichev » Thu May 12, 2011 8:11 am

Below is one with 19 permutations
Code: Select all
........1.....2.3...4.5.6.........2..17...8.53..6......5.1...79.6..8.4..2....3... #puzzle with 19 solutions
98243675.57681.9.413.9.7.824985713.66..329.4..25.481978.3.642..7.92.5.13.4179.568 #weakly minimal UA

Details
Hidden Text: Show
Code: Select all
#pattern                                                                            nClues nSolutions
........1.....2.3...4.5.6.........2..17...8.53..6......5.1...79.6..8.4..2....3...       22      19

#solution                                                                         sNumber nUnavoidables
#unavoidable                                                                       uaSize    unique
982436751576812934134957682498571326617329845325648197853164279769285413241793568       1       1
98243675.57681.9.413.9.7.824985713.66..329.4..25.481978.3.642..7.92.5.13.4179.568       59      y

635897241791462538824351697546918723917234865382675914458126379163789452279543186       2       5
6.5........................5.6...................................................       4       n
.........7.......88.......7......................................................       4       n
...8.7........................9.8.................................7.9............       6       n
...897........................9.87...............7.9.............................       8       n
....97........................9..7...............7.9..............7.9............       8       n

635897241891462537724351698546918723917234865382675914458126379163789452279543186       3       5
6.5........................5.6...................................................       4       n
.........8.......77.......8......................................................       4       n
...8.7........................9.8.................................7.9............       6       n
...897........................9.87...............7.9.............................       8       n
....97........................9..7...............7.9..............7.9............       8       n

735968241691472538824351697546817923917234865382695714458126379163789452279543186       4       2
7...6....6...7...................................................................       4       n
...9.8........................8.7.................................7.9............       6       n

635978241791462538824351697546817923917234865382695714458126379163789452279543186       5       6
6.5........................5.6...................................................       4       n
6...7....7...6...................................................................       4       n
.........7.......88.......7......................................................       4       n
...9.8........................8.7.................................7.9............       6       n
...978........................8.79...............9.7.............................       8       n
...97...........................79...............9.7..............7.9............       8       n

635978241891462537724351698546817923917234865382695714458126379163789452279543186       6       5
6.5........................5.6...................................................       4       n
.........8.......77.......8......................................................       4       n
...9.8........................8.7.................................7.9............       6       n
...978........................8.79...............9.7.............................       8       n
...97...........................79...............9.7..............7.9............       8       n

536897241791462538824351697645918723917234865382675914458126379163789452279543186       7       5
5.6........................6.5...................................................       4       n
.........7.......88.......7......................................................       4       n
...8.7........................9.8.................................7.9............       6       n
...897........................9.87...............7.9.............................       8       n
....97........................9..7...............7.9..............7.9............       8       n

536897241891462537724351698645918723917234865382675914458126379163789452279543186       8       5
5.6........................6.5...................................................       4       n
.........8.......77.......8......................................................       4       n
...8.7........................9.8.................................7.9............       6       n
...897........................9.87...............7.9.............................       8       n
....97........................9..7...............7.9..............7.9............       8       n

536978241791462538824351697645817923917234865382695714458126379163789452279543186       9       5
5.6........................6.5...................................................       4       n
.........7.......88.......7......................................................       4       n
...9.8........................8.7.................................7.9............       6       n
...978........................8.79...............9.7.............................       8       n
...97...........................79...............9.7..............7.9............       8       n

536978241891462537724351698645817923917234865382695714458126379163789452279543186       10      5
5.6........................6.5...................................................       4       n
.........8.......77.......8......................................................       4       n
...9.8........................8.7.................................7.9............       6       n
...978........................8.79...............9.7.............................       8       n
...97...........................79...............9.7..............7.9............       8       n

635798241791462538824351697546819723917234865382675914458126379163987452279543186       11      5
6.5........................5.6...................................................       4       n
.........7.......88.......7......................................................       4       n
...7.8........................8.9.................................9.7............       6       n
...798........................8.97...............7.9.............................       8       n
...79...........................97...............7.9..............9.7............       8       n

635798241891462537724351698546819723917234865382675914458126379163987452279543186       12      5
6.5........................5.6...................................................       4       n
.........8.......77.......8......................................................       4       n
...7.8........................8.9.................................9.7............       6       n
...798........................8.97...............7.9.............................       8       n
...79...........................97...............7.9..............9.7............       8       n

735869241691472538824351697546718923917234865382695714458126379163987452279543186       13      2
7...6....6...7...................................................................       4       n
...8.9........................7.8.................................9.7............       6       n

635879241791462538824351697546718923917234865382695714458126379163987452279543186       14      6
6.5........................5.6...................................................       4       n
6...7....7...6...................................................................       4       n
.........7.......88.......7......................................................       4       n
...8.9........................7.8.................................9.7............       6       n
...879........................7.89...............9.7.............................       8       n
....79........................7..9...............9.7..............9.7............       8       n

635879241891462537724351698546718923917234865382695714458126379163987452279543186       15      5
6.5........................5.6...................................................       4       n
.........8.......77.......8......................................................       4       n
...8.9........................7.8.................................9.7............       6       n
...879........................7.89...............9.7.............................       8       n
....79........................7..9...............9.7..............9.7............       8       n

536798241791462538824351697645819723917234865382675914458126379163987452279543186       16      5
5.6........................6.5...................................................       4       n
.........7.......88.......7......................................................       4       n
...7.8........................8.9.................................9.7............       6       n
...798........................8.97...............7.9.............................       8       n
...79...........................97...............7.9..............9.7............       8       n

536798241891462537724351698645819723917234865382675914458126379163987452279543186       17      5
5.6........................6.5...................................................       4       n
.........8.......77.......8......................................................       4       n
...7.8........................8.9.................................9.7............       6       n
...798........................8.97...............7.9.............................       8       n
...79...........................97...............7.9..............9.7............       8       n

536879241791462538824351697645718923917234865382695714458126379163987452279543186       18      5
5.6........................6.5...................................................       4       n
.........7.......88.......7......................................................       4       n
...8.9........................7.8.................................9.7............       6       n
...879........................7.89...............9.7.............................       8       n
....79........................7..9...............9.7..............9.7............       8       n

536879241891462537724351698645718923917234865382695714458126379163987452279543186       19      5
5.6........................6.5...................................................       4       n
.........8.......77.......8......................................................       4       n
...8.9........................7.8.................................9.7............       6       n
...879........................7.89...............9.7.............................       8       n
....79........................7..9...............9.7..............9.7............       8       n
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Re: puzzle difficulty & largest UA hit by a single clue

Postby RW » Thu May 12, 2011 12:33 pm

Congratulations on the 19! I think a year ago nobody would have expected sets like these to show up...

dobrichev wrote:
RW wrote:... All these moves rely on given clue 2 in r4c6. Remove this clue and none of these singles and locked candidates are available anymore. Now the puzzle has 1242 solutions and not a single cell can be solved.


The 1242 solutions came from 191 unhit UA, one of which is UA51- the largest UA hit by a single clue.

Below are the details for the single clue removed, see clue #9.

Thank you for that. Interesting that the clue hitting the largest UA could easily be predicted by looking at solving moves in the initial grid.

When you present the UA details, would it also be possible to give the amount of unsolved cells that are not included in any unhit UA's? In other words, the amount of cells that can be solved even with the clue removed. I think the sum of these numbers should have some correlation to the difficulty of the puzzle. If the number is large, then you can solve a lot by focusing on only part of the puzzle. If it is very small, then you have to gather information from all over the puzzle to solve any cell.

RW
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Re: puzzle difficulty & largest UA hit by a single clue

Postby dobrichev » Thu May 12, 2011 2:25 pm

RW wrote:When you present the UA details, would it also be possible to give the amount of unsolved cells that are not included in any unhit UA's? In other words, the amount of cells that can be solved even with the clue removed. I think the sum of these numbers should have some correlation to the difficulty of the puzzle. If the number is large, then you can solve a lot by focusing on only part of the puzzle. If it is very small, then you have to gather information from all over the puzzle to solve any cell.


Will do it.
Probably, additionally to the count, you want the puzzle (or mask) with solved (or unsolved) clues in the output.
Please provide an example how the output you want to look like, and I'll code it and publish the tool.
You may continue in Programmers' forum in GridChecker's thread.
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21

Postby dobrichev » Thu May 12, 2011 5:05 pm

21 permutations. What is the theoretical limit?
Code: Select all
........1.....2.3...435.6........5...6..7..2.8..1....9.....3.4..5....7..4.19....8 #puzzle with 21 solutions
93684725.58761.9.421...9.87743298.161.95.48.3.25.3647.69278.1.53.8461.92.7..2536. #weakly minimal UA set


Details
Hidden Text: Show
Code: Select all
#pattern                                                                            nClues nSolutions
........1.....2.3...435.6........5...6..7..2.8..1....9.....3.4..5....7..4.19....8       22      21

#solution                                                                         sNumber nUnavoidables
#unavoidable                                                                       uaSize    unique
523786491716492835984351672192634587365879124847125369278513946659248713431967258       1       3
5.3.................................3.5..........................................       4       n
...78.49.7..49.8..9......7.......................................................       10      n
...786.9.7..49....9......7....6.4..................................48............       13      n

523694871196782435784351692912436587365879124847125369278513946659248713431967258       2       4
5.3.................................3.5..........................................       4       n
...6.4........................4.6................................................       4       n
.........19................91....................................................       4       n
.....48......8.4...................................................48............       6       n

523694871916782435784351692192436587365879124847125369278513946659248713431967258       3       5
5.3.................................3.5..........................................       4       n
...6.4........................4.6................................................       4       n
.........91................19....................................................       4       n
.........9.6...................................................6.9...............       4       n
.....48......8.4...................................................48............       6       n

523496871196782435784351692912634587365879124847125369278513946659248713431967258       4       3
5.3.................................3.5..........................................       4       n
...4.6........................6.4................................................       4       n
.........19................91....................................................       4       n

523496871916782435784351692192634587365879124847125369278513946659248713431967258       5       5
5.3.................................3.5..........................................       4       n
...4.6........................6.4................................................       4       n
.........91................19....................................................       4       n
.........9.6...................................................6.9...............       4       n
...49.87.9..78.4..7......9.......................................................       10      n

325786491716492835984351672192634587563879124847125369278513946659248713431967258       6       3
3.5.................................5.3..........................................       4       n
...78.49.7..49.8..9......7.......................................................       10      n
...786.9.7..49....9......7....6.4..................................48............       13      n

325694871196782435784351692912436587563879124847125369278513946659248713431967258       7       4
3.5.................................5.3..........................................       4       n
...6.4........................4.6................................................       4       n
.........19................91....................................................       4       n
.....48......8.4...................................................48............       6       n

325694871916782435784351692192436587563879124847125369278513946659248713431967258       8       5
3.5.................................5.3..........................................       4       n
...6.4........................4.6................................................       4       n
.........91................19....................................................       4       n
.........9.6...................................................6.9...............       4       n
.....48......8.4...................................................48............       6       n

325496871196782435784351692912634587563879124847125369278513946659248713431967258       9       3
3.5.................................5.3..........................................       4       n
...4.6........................6.4................................................       4       n
.........19................91....................................................       4       n

325496871916782435784351692192634587563879124847125369278513946659248713431967258       10      5
3.5.................................5.3..........................................       4       n
...4.6........................6.4................................................       4       n
.........91................19....................................................       4       n
.........9.6...................................................6.9...............       4       n
...49.87.9..78.4..7......9.......................................................       10      n

325698471196742835784351692912436587563879124847125369278513946659284713431967258       11      3
3.5.................................5.3..........................................       4       n
.........19................91....................................................       4       n
.....84......4.8...................................................84............       6       n

325698471916742835784351692192436587563879124847125369278513946659284713431967258       12      5
3.5.................................5.3..........................................       4       n
.........91................19....................................................       4       n
.........9.6...................................................6.9...............       4       n
.....84......4.8...................................................84............       6       n
...698.7.9..74....7......9....4.6..................................84............       13      n

523698471196742835784351692912436587365879124847125369278513946659284713431967258       13      3
5.3.................................3.5..........................................       4       n
.........19................91....................................................       4       n
.....84......4.8...................................................84............       6       n

523698471916742835784351692192436587365879124847125369278513946659284713431967258       14      5
5.3.................................3.5..........................................       4       n
.........91................19....................................................       4       n
.........9.6...................................................6.9...............       4       n
.....84......4.8...................................................84............       6       n
...698.7.9..74....7......9....4.6..................................84............       13      n

325496871619782435784351692192634587563879124847125369278513946956248713431967258       15      3
3.5.................................5.3..........................................       4       n
...4.6........................6.4................................................       4       n
.........6.9...................................................9.6...............       4       n

325694871619782435784351692192436587563879124847125369278513946956248713431967258       16      4
3.5.................................5.3..........................................       4       n
...6.4........................4.6................................................       4       n
.........6.9...................................................9.6...............       4       n
.....48......8.4...................................................48............       6       n

523496871619782435784351692192634587365879124847125369278513946956248713431967258       17      3
5.3.................................3.5..........................................       4       n
...4.6........................6.4................................................       4       n
.........6.9...................................................9.6...............       4       n

523694871619782435784351692192436587365879124847125369278513946956248713431967258       18      4
5.3.................................3.5..........................................       4       n
...6.4........................4.6................................................       4       n
.........6.9...................................................9.6...............       4       n
.....48......8.4...................................................48............       6       n

325698471619742835784351692192436587563879124847125369278513946956284713431967258       19      3
3.5.................................5.3..........................................       4       n
.........6.9...................................................9.6...............       4       n
.....84......4.8...................................................84............       6       n

523698471619742835784351692192436587365879124847125369278513946956284713431967258       20      3
5.3.................................3.5..........................................       4       n
.........6.9...................................................9.6...............       4       n
.....84......4.8...................................................84............       6       n

936847251587612934214359687743298516169574823825136479692783145358461792471925368       21      1
93684725.58761.9.421...9.87743298.161.95.48.3.25.3647.69278.1.53.8461.92.7..2536.       59      y
dobrichev
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